{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EEVXAHOIXKWVSBT2FZMOKXQHBR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7e9e8d7bbe883164f1a83d349a8a3d5d0075a17498899643d2d886a6dbf20977","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-09-11T20:04:28Z","title_canon_sha256":"7b43d603bce2347cc890e0000c0b54b53230c6bae7140cc80bc7ffe50652b6d0"},"schema_version":"1.0","source":{"id":"2309.05797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.05797","created_at":"2026-07-05T10:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"2309.05797v2","created_at":"2026-07-05T10:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.05797","created_at":"2026-07-05T10:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"EEVXAHOIXKWV","created_at":"2026-07-05T10:56:04Z"},{"alias_kind":"pith_short_16","alias_value":"EEVXAHOIXKWVSBT2","created_at":"2026-07-05T10:56:04Z"},{"alias_kind":"pith_short_8","alias_value":"EEVXAHOI","created_at":"2026-07-05T10:56:04Z"}],"graph_snapshots":[{"event_id":"sha256:a1df6aea971ab2907530cecaad01947d38c7f7c861da9bdf40477d8764e6e3e3","target":"graph","created_at":"2026-07-05T10:56:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.05797/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that any scaling limit of a critical reflection positive Ising or $\\varphi^4$ model of effective dimension $d_{\\text{eff}}$ at least four is Gaussian. This extends the recent breakthrough work of Aizenman and Duminil-Copin -- which demonstrates the corresponding result in the setup of nearest-neighbour interactions in dimension four -- to the case of long-range reflection positive interactions satisfying $d_{\\text{eff}}=4$. The proof relies on the random current representation which provides a geometric interpretation of the deviation of the models' correlation functions from Wick's l","authors_text":"Romain Panis","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-09-11T20:04:28Z","title":"Triviality of the scaling limits of critical Ising and $\\varphi^4$ models with effective dimension at least four"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05797","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f7e174fcca83915615c40441bae8d776998dbec6e19fec64933432a0451cf0a6","target":"record","created_at":"2026-07-05T10:56:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7e9e8d7bbe883164f1a83d349a8a3d5d0075a17498899643d2d886a6dbf20977","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-09-11T20:04:28Z","title_canon_sha256":"7b43d603bce2347cc890e0000c0b54b53230c6bae7140cc80bc7ffe50652b6d0"},"schema_version":"1.0","source":{"id":"2309.05797","kind":"arxiv","version":2}},"canonical_sha256":"212b701dc8baad59067a2e58e55e070c6a9d3be759ca0f9f0a0907ff040072c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"212b701dc8baad59067a2e58e55e070c6a9d3be759ca0f9f0a0907ff040072c7","first_computed_at":"2026-07-05T10:56:04.425479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:56:04.425479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rrbnJXGxsCFfp4BHj55mbmLdazfrL+Y4V1mx9BZMuVeHpUS1MDRTqBo0Ic+zPZy8SdSM4uztWUCMX/hX36fYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:56:04.425833Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.05797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7e174fcca83915615c40441bae8d776998dbec6e19fec64933432a0451cf0a6","sha256:a1df6aea971ab2907530cecaad01947d38c7f7c861da9bdf40477d8764e6e3e3"],"state_sha256":"b303cf2dc0034dde77f942fbfd1c2e5359a4ab4972e406a401d1f56edec380b2"}